What is a Dot, anyway???
We hear about Dots, Spots, Pixels and Lines...always with the "per inch" on the end. This is resolution talk...how many of something are crammed into an inch of image...which gives us the detail we like to see in a print job.
The levels of Gray Thing.
The best place to get the scoop on this is in the Real World Scanning and Halftones book. But, I will give you the quick explanation.
First, you make the images in the computer with scans and shapes and the like.
Second, you send the files into a RIP to make up the bitmapped image of the page that will be written onto film. This bitmapped image is one color, one bit and screamingly high resolution...like 2400 spots per inch.
Third, the RIP sends the bitmapped page to the imagesetter which draws each pixel onto the film with its laser.
The RIP figures out how to make the halftone dots from the information in the pixels of the bitmapped scans or the outlines in the Postscript instructions. The RIP was told by the operator what lpi the halftone will be and the RIP knows how to convert the gray or colored tones in the pixels into the pattern of halftone dots.
To make just one dot...the imagesetter lays out a square on the grid required to make a halftone. For example, a grid square one 133rd of an inch.
The imagesetter can make a number of sizes of dots to mimic tones of gray to our naked eyes. Beginning with the pure white, or no dot at all, and adding dots one by one until the whole grid is filled with black. The number of spots the imagesetter uses to fill the grid gives us the number of gray tones. Gray level one is no spot, level two is one spot, level three is two spots, level four is three spots...and on and on till it is filled.
We need 256 levels of gray to make the full range of tones contained in our computer images. If you fill the one halftone dot grid with 256 spots you will have 16 across and 16 down. 256=16x16. If the imagesetter can make at least 16 linear spots in every dot of the halftone you are in good shape...256 grays, plus white. A 200 lpi halftone has 200x16 spots every inch. That is 3200 spots per inch. If the imagesetter can make that many spots you get all 256 levels.
If your imagesetter only makes 2400 spots per inch, you would need to make bigger halftone dots to get all the levels. 2400 divided by 16 gives 150 grids for halftone dots... a 150 lpi screen.
The Quality Factor Thing...
If everything was horizontal and vertical in this world, we could use one pixel to make one halftone dot. But this is the real world. The printers found that a halftone made the best rendition of most images if it ran at a 45 degree angle. It gives smoother edges to horizontal and vertical details. When they print process color, the dots are angled all over, mostly at 30 degree variations.
They also discovered that it took more than one pixel to make a good looking dot when the dots ran at 45 degrees to the pattern of pixels in the scans. This is the quality factor. If you give the RIP from 2 to 1.2 times the lpi count of halftone dots in your scan the halftone will look its best.
Low lpi (85 lpi)images benefit from the 2 times factor. A 200 lpi screen is usually OK with a 1.2 factor.
And that is the quick halftone story...hopefully told with as few levels of gray area as possible.